Your speculations raise a larger question: Can you think without language? Answer: Nope, at least not at the level humans are accustomed to. That's why deafness can have far more serious consequences than blindness, developmentally speaking. The blind suffer many hardships, not the least of which is the inability to read in the usual manner. But even those sightless from birth acquire language by ear without difficulty in infancy, and having done so lead relatively ordinary lives. A congenitally deaf child isn't so lucky: unless someone realizes very early that he's not talking because he can't hear, his grasp of communication may never progress beyond the rudiments.
The language of the deaf is a vast topic that has filled lots of books--one of the best is Seeing Voices: A Journey Into the World of the Deaf by Oliver Sacks (1989). All I can do in this venue is sketch out a few basic propositions:
The folks at issue here are both (a) profoundly and (b) prelingually deaf. If you don't become totally deaf until after you've acquired language, your problems are . . . well, not minor, but manageable. You think in whatever spoken language you've learned. Given some commonsense accommodation during schooling, you'll progress normally intellectually.
Depending on circumstances you may be able to speak and lip-read.
About one child in a thousand, however, is born with no ability to hear whatsoever. Years ago such people were called deaf-mutes. Often they were considered retarded, and in a sense they were: they'd never learned language, a process that primes the pump for much later development. The critical age range seems to be 21 to 36 months. During this period children pick up the basics of language easily, and in so doing establish essential cognitive infrastructure. Later on it's far more difficult. If the congenitally deaf aren't diagnosed before they start school, they may face severe learning problems for the rest of their lives, even if in other respects their intelligence is normal.
The profoundly, prelingually deaf can and do acquire language; it's just gestural rather than verbal. The sign language most commonly used in the U.S. is American Sign Language, sometimes called Ameslan or just Sign. Those not conversant in Sign may suppose that it's an invented form of communication like Esperanto or Morse code. It's not. It's an independent natural language, evolved by ordinary people and transmitted culturally from one generation to the next. It bears no relationship to English and in some ways is more similar to Chinese--a single highly inflected gesture can convey an entire word or phrase. (Signed English, in which you'll sometimes see words spelled out one letter at a time, is a completely different animal.) Sign can be acquired effortlessly in early childhood--and by anyone, not just the deaf (e.g., hearing children of deaf parents). Those who do so use it as fluently as most Americans speak English. Sign equips native users with the ability to manipulate symbols, grasp abstractions, and actively acquire and process knowledge--in short, to think, in the full human sense of the term. Nonetheless, "oralists" have long insisted that the best way to educate the deaf is to teach them spoken language, sometimes going so far as to suppress signing. Sacks and many deaf folk think this has been a disaster for deaf people.
The answer to your question is now obvious. In what language do the profoundly deaf think? Why, in Sign (or the local equivalent), assuming they were fortunate enough to have learned it in infancy. The hearing can have only a general idea what this is like--the gulf between spoken and visual language is far greater than that between, say, English and Russian. Research suggests that the brain of a native deaf signer is organized differently from that of a hearing person. Still, sometimes we can get a glimpse. Sacks writes of a visit to the island of Martha's Vineyard, where hereditary deafness was endemic for more than 250 years and a community of signers, most of whom hear normally, still flourishes. He met a woman in her 90s who would sometimes slip into a reverie, her hands moving constantly. According to her daughter, she was thinking in Sign. "Even in sleep, I was further informed, the old lady might sketch fragmentary signs on the counterpane," Sacks writes. "She was dreaming in Sign."
